List of practice Questions

The ratio of speeds of a motor boat and that of current of water is 35:6. The boat goes against the current in 6 hours 50 minutes. The time taken by boat to come back is :

A tank can be filled by two pipes A and B in 18 minutes and 24 respectively. Another tap C can empty the full tank in 36 mintues. If the tap C is opened 6 minutes after the pipes A and B are opened, the tank will become full in a total of :

A retailer has 900 kg of wheat, a part of which he sells at 10% loss and the remaining at a profit of 8%. Overall, he makes a profit of 6%, the quantity sold at profit is :

Value of 2⁴⁸ (mod 15) is :

The direction cosines of a line which makes equal angles with the co-ordinate axes is/are :

If \(\vec{a}\) and \(\vec{b}\) are two non zero vectors such that \(|\vec{a}|\)=10, \(|\vec{b}|=2\) and \(\vec{a}.\vec{b}=12\), then value of \(|\vec{a}\times\vec{b}|\) is :

If xy = e^(x-y), then the value of \(\frac{dy}{dx}\) at (1, 1) is :

Set A has elements and the set B has 6 elements, then the number of injective mappings that can be defined from A to B is :

Which of the following are not the probability distribution of a random variable ?
A.

X	0	1	2
P(X)	0.4	0.4	0.2

B.

X	0	1	2	3	4
P(X)	0.4	0.4	0.2	-0.1	0.3

C.

Y	-1	0	1
P(Y)	0.6	0.1	0.2

D.

Z	3	2	1	0	-1
P(Z)	0.3	0.2	0.4	0.1	0.05

E.

X	0	1	2
P(X)	\(\frac{25}{36}\)	\(\frac{10}{36}\)	\(\frac{1}{36}\)

Choose the correct answer from the options given below :

In a box, consisting 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is :

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (0, 4), (4, 0), (2, 4) and (0, 5). If the maximum value of Z = ax + by where a, b > 0 occurs at both (2, 4) and (4, 0) then

Which of the following statements is true ?
A. If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.
B. Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
C. In a LPP, the minimum value of the objective function Z = ax + by (a, b > 0) is always 0 if origin is one of the corner points of feasible region.
D. In a LPP the max value of the objective function Z = ax + by is always finite.
Choose the correct answer from the options given below :

The angle at which the normal to the plane 4x - 8y + z = 7 is inclined to y-axis is :

If each side of a cube is x, then the angle between the diagonals of the cube is :

ABCD is a rhombus, whose diagonals intersect at E. Then \(\overrightarrow{EA}+\overrightarrow{EB}+\overrightarrow{EC}+\overrightarrow{ED}\) equals to :

The vectors \(3\hat{i}-\hat{j}+2\hat{k},2\hat{i}+\hat{j}+3\hat{k}\) and \(\hat{i}+λ\hat{j}-\hat{k}\) are coplanar if λ is :

The general solution of the differential equation xdy - ydx - 0 represents :

Match List I with List II

List I		List II
A.	\(\frac{d^2y}{dx^2}+(\frac{dy}{dx})^{\frac{1}{2}}+x^{\frac{1}{2}}\)	I.	order 2, degree 1
B.	\(\frac{dy}{dx}=\frac{x^{\frac{1}{2}}}{y^{\frac{1}{2}}(1+x)^{\frac{1}{2}}}\)	II.	order 2, degree not defined
C.	\(\frac{d^2y}{dx^2}=\cos3x+\sin3x\)	III.	order 2, degree 4
D.	\(\frac{d^2y}{dx^2}+2\frac{dy}{dx}+y=\log(\frac{dy}{dx})\)	IV.	order 1, degree 2

Choose the correct answer from the options given below :

The value of the integral \(\int\frac{1-\sin x}{\cos^2 x}dx\) is :

A flight from Delhi to Mumbai leaves every 5 hours. At the evening counter, it clarify that flight took off 25 minutes ago. If the time now is 10:40 am, what is the time for the next flight ?

Consider the table below on the quantities of commodities alongside their prices in the year 2020 and 2022.

Commodity	Prices (₹)		Quantities
	In 2020 Year	In 2022 Year	In 2020 Year	In 2022 Year
A	1	2	5	6
B	3	4	3	4
C	5	6	2	5
D	4	5	1	3
E	3	4	4	6

The value of ∑p₁q₀ is :

The following data is taken from a simple random sample :
3, 7, 5, 9, 15, 11, 8, 4, 6, 2
The point estimate of the population standard deviation is :

For a certain data test statistic ‘t’ is calculated as : \(|t|=|\frac{65-68}{\frac{4}{\sqrt{15}}}|=2.90\), then select the correct option :

Suppose that a 95% confidence interval states that population mean is greater than 100 and less than 300. Then the value of sample mean \((\bar{x})\) and margin of error (E) respectively are :

A machine costing ₹ one lakh depreciates at constant rate 10%. Estimated useful life of machine is 8 years.
Match List I with List II

List I		List II
A.	Total depreciation in 2nd and 3rd year is	I.	₹81,000
B.	Value of machine after one year is	II.	₹17,100
C.	Value of machine after 2 year is	III.	₹43050
D.	Scrap value of machine is : given (1.1)3 - 2.144 & (0.9)3 - 0.4305	IV.	₹90,000

Choose the correct answer from the options given below :